With no time limit, wouldn't it be easier to go back earlier in history to the other steppe tribes from which the Kazakh descend? Or does the OP want it to be obviously Kazakh, and a descendant of the Khanate? (Considering how much they raided both Russia and Persia, one of the nations would eventually do something about it.
In the end, you'd either need to make them a nation that can withstand a prolonged attack from a middle or greater power, eliminate nearby nations that could do such a thing, or put them in a position where they have a noticeable ally nearby. Of course, for Kazakhstan, a wank would just involve them existing for a large portion of the past five hundred years.
Granted, could a large Kazakhstan (a united Tartary, especially both Russian and Chinese parts) successfully play Russia, China, and Persia off of each other? Especially if they settle down and stop being a nomadic nation. No idea how to pull it off, though.